1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Last part of question on continuous functions

  1. Apr 20, 2010 #1
    1. The problem statement, all variables and given/known data
    This is the last part of a revision question I'm trying, would really like to get to the end so any pointers or help would be greatly appreciated.

    Suppose h:(0,1)-> satisfies the following conditions:
    for all xЭ(0,1) there exists d>0 s.t. for all x'Э(x, x+d)n(0,1) we have h(x)<=h(x')

    Prove that if h is continuous on (0,1) then h(x)<=h(y) whenever x.yЭ(0,1) and x<=y. Use a counterexample to show that this results may not be true when h is continuous.

    2. Relevant equations
    Well, definition of continuous functions,
    also above in the question i am asked to state the intermediate value theorem so i think perhaps i am meant to use that.


    3. The attempt at a solution

    if h is continuous on (0,1) then for all cЭ(0,1), for all E>0, Эd s.t. for all xЭ(0,1), 0<|x-c|<d this implies that |h(x)-h(c)|<E
    i really just don't see how to continue. Any help would be great. Thank you
     
  2. jcsd
  3. Apr 20, 2010 #2

    Office_Shredder

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Try fixing x, and showing that for every value of y larger than it, h(x)<=h(y)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Last part of question on continuous functions
Loading...